A Haar wavelet multi-resolution collocation method for singularly perturbed differential equations with integral boundary conditions

Muhammad Ahsan, Martin Bohner, Aizaz Ullah, Amir Ali Khan and Sheraz Ahmad

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 204, issue C, 166-180

Abstract: The focus of this paper is to develop and improve a higher-order Haar wavelet approach for solving nonlinear singularly perturbed differential equations with various pairs of boundary conditions like initial, boundary, two points, integral and multi-point integral boundary conditions. The theoretical convergence and computational stability of the method is also presented. The comparison of the proposed higher-order Haar wavelet method is performed with the recent published work including the well-known Haar wavelet method in terms of convergence and accuracy. In the nonlinear case, a quasilinearization technique has been adopted. The proposed method is easy to implement on various boundary conditions, and the computed results are high-order accurate, stable and efficient. We have also checked the satisfactory performance of the proposed method for nonlinear differential equations having no analytical solution in some of the test problems.

Keywords: Haar wavelet; Singularly perturbed differential equations; Collocation method; Quasilinearization (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:204:y:2023:i:c:p:166-180

DOI: 10.1016/j.matcom.2022.08.004

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